Microscopic insight into the pump-probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

摘要

Here we present a quantum-statistical formulation of relaxation dynamics of superconductors related to pump-probe (PP) spectroscopy. The method is based on the perturbation expansion of the non-equilibrium density matrix for calculation of multi-time correlation functions, and the corresponding response function. As a model for our study, the high-temperature superconductor MgB2 has been selected. Knowledge of the electronic structure and of the corresponding Eliashberg function of electron-phonon (EP) interactions enabled us to distinguish non-equilibrium processes in a sequence of interactions with laser pulses on a microscopic level. Temperature-dependent relaxation dynamics as a function of delay time between the pump and probe pulses have been derived. We have shown that an abrupt increase of the relaxation time at T-c is the direct consequence of sudden changes in the character of EP coupling in transition from an adiabatic to a stabilized superconducting anti-adiabatic state, as it predicts the anti-adiabatic theory of electron-vibration interactions. The BCS model, which is based on adiabatic character of EP coupling, is basically unable to reflect the enormous sudden increase of the relaxation time at T-c. Differences in the optical pump-optical probe and the optical pump-terahertz probe settings of PP relaxation dynamics are discussed within diagrammatic perturbation theory. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim